{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Definitions for automated trading"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Equity Curve and Return Series"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "An equity curve is the traditing account value (Y) plotted against time (X). Otherwise, can be described as the cash at hand + equity value of portfolio asset (Y) against time (X). The goal is to get it to rise linearly with time without reinvestment of gains or rise exponentially with reinvested gains.\n",
    "\n",
    "The *return series* is a list of returns to the account at each trading period. This doesn't depend on the gains."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Characteristics of Equity Curve"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\begin{align}\n",
       "P_{t_0}& : \\text{dollar value of porfolio \\textbf{before} adjustment.} \\\\\n",
       "P_{t_1}& : \\text{dollar value of porfolio \\textbf{after} adjustment} \\\\\n",
       "\\text{for t} & = 0,1,2,\\dots,T \\ \\ \\text{where $t = 0$ represents beginning of simulation and $t = T$ represents current time}\n",
       "\\end{align}"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%latex\n",
    "\\begin{align}\n",
    "P_{t_0}& : \\text{dollar value of porfolio \\textbf{before} adjustment.} \\\\\n",
    "P_{t_1}& : \\text{dollar value of porfolio \\textbf{after} adjustment} \\\\\n",
    "\\text{for t} & = 0,1,2,\\dots,T \\ \\ \\text{where $t = 0$ represents beginning of simulation and $t = T$ represents current time}\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "We assume that portfolio adjustment occurs instantaenously in time. The change in $P$ from $t_0$ to $t_1$ represents change\n",
       "due to adjustment, while change in $P$ from $(t-1)_1$ to $t_0$ is a change due to movement of market prices of assets \n",
       "in the portfolio.This is how $t$ evolves:\n",
       "$$ t_0, t_1, (t+1)_0, (t+1)_1, (t+2)_1,\\dots,T_0, T_1$$ \n",
       "with transition from $t_0$ to $t_1$ occuring instantaneously as the algorithm adjusts the portfolio"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%latex\n",
    "We assume that portfolio adjustment occurs instantaenously in time. The change in $P$ from $t_0$ to $t_1$ represents change\n",
    "due to adjustment, while change in $P$ from $(t-1)_1$ to $t_0$ is a change due to movement of market prices of assets \n",
    "in the portfolio.This is how $t$ evolves:\n",
    "$$ t_0, t_1, (t+1)_0, (t+1)_1, (t+2)_1,\\dots,T_0, T_1$$ \n",
    "with transition from $t_0$ to $t_1$ occuring instantaneously as the algorithm adjusts the portfolio"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now define $C_0$ as the initial cash, $C_{t_0}$ and $C_{t_1}$ as uninvested cash at $t_0$ and $t_1$, and $K_{t}$ as trading costs incurred during instataneous adjustment from $t_0$ to $t_1$. The equity curve at time $t_0$ is equal to the following: $$ E_{t_{0}} = C_{t_0} + P_{t_0}= C_{0} + \\sum_{i=1}^{t} \\left \\{ P_{i_0} - P_{(i-1)_{1}} - K_{i-1} \\right \\}$$\n",
    "Note that $C_0 = C_{t_0}$ when $t = 0$. Further, the difference between $E_{t_1}$ and $E_{t_0}$ is the total trading costs incurred during the adjustment period from $t_0$ to $t_1$:\n",
    "$$ E_{t_1} = E_{t_0} - K_t$$\n",
    "Only the $E_{t_1}$ is plotted in the *equity curve* which reflects the impact of commission and other costs associated with adjustment from $t_0$ to $t_1$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Characteristics of Return Series"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$V_t$: tradable capital at time $t_0$. This value is set by the trader. Total cash invested can't exceed $V_t$ at any time. Define $t(i_1)$ and $t(i_0)$ to be times $t_1$ and $t_0$ at which trade $i$ was initiated and exited, respectively. Trade $i$ is considered to be active at time $t$ if $t(i_1) \\leq t_1 \\lt t(i_0)$. $i \\in I_t$ if $i$ is active at $t_1$. Define $j_i$ as asset initiated in trade $i$. Allow $P_{t_0}$ and $P_{t_1}$ to be subsettable by asset such tat $P_{t_1,j}$ represent the value of asset $j$ in the portfolio at time $t_1$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If 5 trades were exectued, then there would be 5 new $i$'s subsettable to $t$ fo these transactions. Infinitely many overlapping trades can be made and be described as the previous notation.\n",
    "\n",
    "The tradable capital must meet the following condition for all $t = 0,1,\\dots,T$:\n",
    "$$V_t \\ge \\sum_{i \\in I_t} P_{t(i)_{1}),j_i}$$\n",
    "$V_t$ would be determined during or prior to $(t-1)$ based on the information we have (e.g. current cash and gains from previous trades and market movement)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Verbally the above indicates that the sum of the initial purchase price of all active trades are less than or requal to the tradable capital. However, there is no restriction regarding the relationship between $V_t$ and $P_{t_1}$ and  $P_{t_0}$ because $P_{t_1}$ and  $P_{t_0}$ are current market value of the portfolio rather than the initial price. The definition of $V_t$ is defined as above such that:\n",
    "\n",
    "- $V_t$ is determined algorithmically before adjustment period\n",
    "- Return series penalized for allocating more capital than is invested.\n",
    "- ALlow flexibility in tradable capital rather than enforce strict constancy or compounding"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The equation for return series is as follows:\n",
    "$$ R_t = \\frac{P_{t_0} - P_{(t-1)_1} - K_{(t-1)}}{V_{t-1}}$$\n",
    "This equation is different from the classical definition of return series: percentage change in equity curve from $(t-1)$ to $t$ which fails to take into account the following:\n",
    "\n",
    "- If cash winthdrawals or deposits are made to the trading account after $t = 0$. Here the denominator (i.e. tradable capital) takes that into account with the new equation\n",
    "- If earnings are not strictly reinvested. (Again the $V_(t-1)$ takes into account but also the commisions $(K_{(t-1)})$ takes into account the reinvested earnings-based commission/fee.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Risk-Return Metrics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The idea is to maximize risk-adjusted return. The strategy would be to develop models by backtesting (or basically cross-validating and selecting parameters that best fit to get best prediction model).Many measures of risk-adjusted return can be selected as the outcome..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**High-Frequency Sharpe Ratio**: $Sharpe = \\frac{\\bar{R}}{\\sigma_R}$, where $\\bar{R} = \\frac{R_1+,\\dots,+R_T}{T}$ and $\\sigma_R = \\sqrt{\\frac{1}{T-1} \\sum (R_t - \\bar{R})}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are others but will go over during coding :)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Characteristics of Risk-Return Metrics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Equity curves will be simulated to study characteristics of risk-return metrics. This will help in determining which risk-return metric to focus on.\n",
    "Generate equity curve using SPY returns and random numbers with constant tradable capital of \\$10,000. For this exercise use only $E_{t_0}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "%load_ext rpy2.ipython"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.6/dist-packages/rpy2/rinterface/__init__.py:145: RRuntimeWarning: Loading required package: xts\n",
      "\n",
      "  warnings.warn(x, RRuntimeWarning)\n",
      "/usr/local/lib/python3.6/dist-packages/rpy2/rinterface/__init__.py:145: RRuntimeWarning: Loading required package: zoo\n",
      "\n",
      "  warnings.warn(x, RRuntimeWarning)\n",
      "/usr/local/lib/python3.6/dist-packages/rpy2/rinterface/__init__.py:145: RRuntimeWarning: \n",
      "Attaching package: ‘zoo’\n",
      "\n",
      "\n",
      "  warnings.warn(x, RRuntimeWarning)\n",
      "/usr/local/lib/python3.6/dist-packages/rpy2/rinterface/__init__.py:145: RRuntimeWarning: The following objects are masked from ‘package:base’:\n",
      "\n",
      "    as.Date, as.Date.numeric\n",
      "\n",
      "\n",
      "  warnings.warn(x, RRuntimeWarning)\n",
      "/usr/local/lib/python3.6/dist-packages/rpy2/rinterface/__init__.py:145: RRuntimeWarning: Loading required package: TTR\n",
      "\n",
      "  warnings.warn(x, RRuntimeWarning)\n",
      "/usr/local/lib/python3.6/dist-packages/rpy2/rinterface/__init__.py:145: RRuntimeWarning: Version 0.4-0 included new data defaults. See ?getSymbols.\n",
      "Learn from a quantmod author: https://www.datacamp.com/courses/importing-and-managing-financial-data-in-r\n",
      "\n",
      "  warnings.warn(x, RRuntimeWarning)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array(['quantmod', 'TTR', 'xts', 'zoo', 'tools', 'stats', 'graphics',\n",
       "       'grDevices', 'utils', 'datasets', 'methods', 'base'],\n",
       "      dtype='<U9')"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%R library(quantmod)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.6/dist-packages/rpy2/rinterface/__init__.py:145: RRuntimeWarning: \n",
      "WARNING: There have been significant changes to Yahoo Finance data.\n",
      "Please see the Warning section of ‘?getSymbols.yahoo’ for details.\n",
      "\n",
      "This message is shown once per session and may be disabled by setting\n",
      "options(\"getSymbols.yahoo.warning\"=FALSE).\n",
      "\n",
      "  warnings.warn(x, RRuntimeWarning)\n"
     ]
    }
   ],
   "source": [
    "%%R \n",
    "options(\"getSymbols.warning4.0\"=FALSE,\n",
    "            \"getSymbols.auto.assign\"=FALSE)\n",
    "# Load S&P 500 ETF data, stores closing prices as a vector\n",
    "SPY <- suppressWarnings(\n",
    "    getSymbols(c(\"SPY\"), from = \"2012-01-01\"))\n",
    "SPY <- as.numeric(SPY$SPY.Close)[1:987]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The data for SPY has been acquired and prepared. We can simulate the equity curve and study some of the characteristics of risk-return metrics. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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GQ6/v+p133ikrKxs2bFivbxmDblbvjz/+2GKxXHfddQN9IHHEjBkz1q9fLxQOsmdtOFwu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3FsWaFQYAjMcVxTU9Ndd91FUdSRI0c++uijgJ0iQRcWFuLtoVAocIXm5mZUw+MY8JaXl1dWVoZ7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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%R\n",
    "# Set seed\n",
    "\n",
    "\n",
    "set.seed(1)\n",
    "# Create time index\n",
    "t <- 1:(length(SPY) - 1)\n",
    "    \n",
    "# Tradable capital vector\n",
    "Vt <- c(rep(1e4, length(t)))\n",
    "\n",
    "# Return Series\n",
    "# benchmark return series\n",
    "Rb <- rep(NA, length(t))\n",
    "\n",
    "# Randomly Generate return series 1 and 2\n",
    "Rt <- rep(NA, length(t))\n",
    "Rt2 <- rep(NA, length(t))\n",
    "\n",
    "\n",
    "# Equity Curves\n",
    "# benchmark equity curve\n",
    "Eb <- rep(NA, length(t))\n",
    "Eb[1] <- Vt[1]\n",
    "\n",
    "# Randomly Generate Equity CUrve 1 and 2 \n",
    "\n",
    "Et <- rep(NA, length(t))\n",
    "Et <- Vt[1]\n",
    "Et2 <- rep(NA, length(t))\n",
    "Et2 <- Vt[1]\n",
    "\n",
    "for(i in 2:length(t)){\n",
    "    \n",
    "    # First simulate the Return serires \n",
    "    Rb[i] <- (SPY[i]/SPY[i-1]) - 1\n",
    "\n",
    "    # Then simulate the equity curves\n",
    "    Eb[i] <- Eb[i-1]*(1+Rb[i])\n",
    "    \n",
    "    \n",
    "}\n",
    "\n",
    "for(i in 2:length(t)){\n",
    "    # First simulate the Return serires \n",
    "    Rt[i] <- Rb[i] + rnorm(n = 1, mean = 0.24/length(t), sd=2.5*sd(Rb,na.rm=TRUE))\n",
    "    \n",
    "    Rt2[i] <- Rb[i] + rnorm(n = 1, mean = 0.02/length(t), sd=0.75*sd(Rb,na.rm=TRUE))\n",
    "    \n",
    "    # Then simulate the equity curves\n",
    "    Et[i] <- Et[i-1]*(1+Rt[i])\n",
    "    \n",
    "    Et2[i] <- Et2[i-1]*(1+Rt2[i])\n",
    "}\n",
    "\n",
    "plot(y = Et, x = t, type = \"l\", col = 1,\n",
    "    xlab = \"Time\",\n",
    "    ylab = \"Equity ($)\",\n",
    "    main = \"Randomly Generated Equity Curves\")\n",
    "grid()\n",
    "abline(h = 1e4)\n",
    "lines(y = Et2, x = t, col = 2)\n",
    "lines(y = Eb, x = t, col = 8)\n",
    "legend( x = \"topleft\", col = c(1,2,8), lwd = 2, legend = c(\"Curve 1\", \"Curve 2\", \"SPY\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sharp Ratio"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The high frequency sharp ratio only uses the $\\bar{R}$ in the numerator instead of subtracting the $\\bar{R} - R_j$ which is the risk free/benchmark return (i.e. the Excess return = Portfolio return - Benchmark return). This metric would be useful to those that are trading high frequency at least once a day or more."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%R\n",
    "# The equation again would be average excess return / sd return\n",
    "# High frequency Sharp Ratio ignore the NA's\n",
    "SR <- mean(Rt, na.rm=TRUE) / sd(Rt, na.rm = TRUE) \n",
    "SR2 <- mean(Rt2, na.rm=TRUE) / sd(Rt2, na.rm = TRUE) \n",
    "SRb <- mean(Rb, na.rm=TRUE) / sd(Rb, na.rm = TRUE) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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UVDz66KPD0DomusC5OKIUnIsjFAyH7Pjdd981NjZ6VUW5XH7DDTdMnDgxOzt7GFrHRBd4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AgEDoeDyWR2dnZu27aNHKPl5OQoFAoyQY8cORIAUCCJIJfLa2pqUPEhsdBoNPpt8sThcGw22xWG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\nAABJRU5ErkJggg==\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%R\n",
    "plot(y = Et, x =t , type = 'l', col = 1,\n",
    "    xlab = \"\",\n",
    "    ylab = \"Equity ($)\",\n",
    "    main = \"Sharp Ratios\",\n",
    "    ylim = c(6e3,1.9e4))\n",
    "grid()\n",
    "abline(h = 1e4)\n",
    "lines(y = Et2, x = t, col =2)\n",
    "lines(y = Eb, x = t, col = 8)\n",
    "legend(x = \"topleft\", col = c(1,2,8), lwd = 2,\n",
    "      legend = c(paste0(\"SR = \", round(SR, 3)),\n",
    "                paste0(\"SR = \", round(SR2, 3)),\n",
    "                paste0(\"SR = \", round(SRb, 3))))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that the 1st simulated curve has the lowest overall return and Sharp ratio. The highest return (red) also has a high SR but similar SR is visible from the SYP index. Note Sharp Ratio:\n",
    "\n",
    "- Penalizes for large losses and large gains (i.e. variance in the denominator)\n",
    "- Since the formula exhibits similar statistical form to Z or T score, the returns are assumed to be normally distributed\n",
    "- The denominator benchmarks against the mean return (as seen in the $\\sigma_R$ equation) but the numerator standardizes against a completely separate benchmark (in this case 0 as high frequency doesn't benchmark against the standard). "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now since I'm interested in Bitcoin and other cryptocurrency I will also look into that now."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%R\n",
    "\n",
    "# Load S&P 500 ETF data, stores closing prices as a vector\n",
    "BTC <- suppressWarnings(\n",
    "    getSymbols(c(\"BTC-USD\"), from = \"2012-01-01\"))\n",
    "\n",
    "BTC <- as.numeric(BTC[,4])[1:987] # 4th column is the closing column"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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162exWCRtoDGCEWYGWnhOnz6NVgvsQlRXs3fdxbIsO28eC8A6rFjtmVdeYX/4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\nZgM2rgZbUIDvvkN4OESiJmltLoGWSESE4KpAE0J4S0StVq/ZufMnPj+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r66FQ4JlnYLV6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\nTaFQKN0UKtAUCoXSTfl/uUnLorKyCaEAAAAASUVORK5CYII=\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%R\n",
    "\n",
    "set.seed(1)\n",
    "# Create time index\n",
    "t <- 1:(length(BTC) - 1)\n",
    "    \n",
    "# Tradable capital vector\n",
    "Vt <- c(rep(1e4, length(t)))\n",
    "\n",
    "# Return Series\n",
    "# benchmark return series\n",
    "Rb <- rep(NA, length(t))\n",
    "\n",
    "# Randomly Generate return series 1 and 2\n",
    "Rt <- rep(NA, length(t))\n",
    "Rt2 <- rep(NA, length(t))\n",
    "\n",
    "\n",
    "# Equity Curves\n",
    "# benchmark equity curve\n",
    "Eb <- rep(NA, length(t))\n",
    "Eb[1] <- Vt[1]\n",
    "\n",
    "# Randomly Generate Equity CUrve 1 and 2 \n",
    "\n",
    "Et <- rep(NA, length(t))\n",
    "Et <- Vt[1]\n",
    "Et2 <- rep(NA, length(t))\n",
    "Et2 <- Vt[1]\n",
    "\n",
    "for(i in 2:length(t)){\n",
    "    \n",
    "    # First simulate the Return serires \n",
    "    Rb[i] <- (BTC[i]/BTC[i-1]) - 1\n",
    "\n",
    "    # Then simulate the equity curves\n",
    "    Eb[i] <- Eb[i-1]*(1+Rb[i])\n",
    "    \n",
    "    \n",
    "}\n",
    "\n",
    "for(i in 2:length(t)){\n",
    "    # First simulate the Return serires \n",
    "    Rt[i] <- Rb[i] + rnorm(n = 1, mean = 2/length(t), sd=0.5*sd(Rb,na.rm=TRUE))\n",
    "    \n",
    "    Rt2[i] <- Rb[i] + rnorm(n = 1, mean = 4/length(t), sd=0.75*sd(Rb,na.rm=TRUE))\n",
    "    \n",
    "    # Then simulate the equity curves\n",
    "    Et[i] <- Et[i-1]*(1+Rt[i])\n",
    "    \n",
    "    Et2[i] <- Et2[i-1]*(1+Rt2[i])\n",
    "}\n",
    "\n",
    "SR <- mean(Rt, na.rm=TRUE) / sd(Rt, na.rm = TRUE) \n",
    "SR2 <- mean(Rt2, na.rm=TRUE) / sd(Rt2, na.rm = TRUE) \n",
    "SRb <- mean(Rb, na.rm=TRUE) / sd(Rb, na.rm = TRUE) \n",
    "\n",
    "plot(y = Et, x = t, type = \"l\", col = 1,\n",
    "    xlab = \"Time\",\n",
    "    ylab = \"Equity ($)\",\n",
    "    main = \"Randomly Generated Equity Curves\",\n",
    "    ylim = c(0, 2.5e6))\n",
    "grid()\n",
    "abline(h = 1e4)\n",
    "lines(y = Et2, x = t, col = 2)\n",
    "lines(y = Eb, x = t, col = 8)\n",
    "legend( x = \"topleft\", col = c(1,2,8), lwd = 2, legend = c(paste0(\"Curve 1 SR = \",round(SR,3)),\n",
    "                                                           paste0(\"Curve 2 SR = \",round(SR2,3)),\n",
    "                                                           paste0(\"BTC-USD SR = \",round(SRb,3))))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that based on the difference in the mean random value we add, the 2nd curve gets us the greatest return in addition to the highest SR. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Maximum Drawdown Ratios"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Maximum dradown (MD) represents the most \\$ lost in equity by a strategy from any point to any point in the future (during the period in the future. It is a measure of risk (because it represents the maximum lost a strategy has incurred) and behaves like a variance term when multiple (i.e. $n$) dradowns are aggregated in some way."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The formula is short:\n",
    "$$ \\text{MD} = \\max(E_{k_1} -  E_{l_1} \\ \\ \\text{for} k \\lt l \\lt T $$\n",
    "Notice that here we are using both $E_{k_1} -  E_{l_1}$ where we only need to use one vector after adjustment but usually the equation would be \n",
    "$$ \\text{MD} = \\max(E_{k_0} -  E_{l_1} \\ \\ \\text{for} k \\lt l \\lt T $$\n",
    "which would require two equity curves $E_{t_0}$ and $E_{t_1}$. For simplicity we only use the after adjustement equity curve (i.e. $E_{t_1}$)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%R\n",
    "\n",
    "MD <- function(curve, n = 1){\n",
    "    time <- length(curve)\n",
    "    v <- rep(NA, (time*(time-1))/2)\n",
    "    k <- 1\n",
    "    \n",
    "    for(i in 1:(length(curve)-1)){\n",
    "        # This inner loop will compare all of the time i curve value with time j curve values\n",
    "        for(j in (i+1):length(curve)){\n",
    "            v[k] <- curve[i] - curve[j]\n",
    "            k <- k + 1\n",
    "        }\n",
    "    }\n",
    "    m <- rep(NA, length(n))\n",
    "    \n",
    "    for(i in 1:n){\n",
    "        m[i] <- max(v)\n",
    "        v[which.max(v)] <- -Inf\n",
    "    }\n",
    "    return(m)\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The function essentially takes the equity curve and returns a vector of length *n* of drawdown values. If $n = 1$ then that would be the maximum drawdawn value. Here are a few performance measures that uses MD.\n",
    "\n",
    "$$ \\text{NPMD} = \\frac{E_{T_0} - V_0}{\\text{MD}} \\\\\n",
    "\\text{Burke}_n = \\frac{E_{T_0} - V_0}{({\\frac{1}{T}\\sum_{i=1}^n \\text{MD}_i ^{2}})^\\frac{1}{2}}  $$\n",
    "\n",
    "The High Frequency Burke metric is basically an attempt at improving on the Sharpe Ratio by utilizing the squared sum of the $n$ largest MD as a variance term. The ratios are not highly standardizes so either mean return or total dollar return can be used as the numerator. The below code will utilize total dollar return for both metrics."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%R\n",
    "\n",
    "# Net Profit to Max Drawdown Ratio and Burke calculation\n",
    "\n",
    "NPMD <- (Et[length(Et)] - Vt[1]) / MD(Et)\n",
    "Burke <- (Et[length(Et)] - Vt[1]) / sqrt((1/length(Et))* sum(MD(Et, n = round(length(Et)/20))^2))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "          [,1]       [,2]     [,3]\n",
       "[1,] 0.4195952 0.01552739 1.200108\n",
       "[2,] 2.1387106 0.07109052 6.359643\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%R\n",
    "sapply(list(Eb, Et, Et2), function(x) {\n",
    "    NPMD <- (x[length(x)] - Vt[1]) / MD(x)\n",
    "    Burke <- (x[length(x)] - Vt[1]) / sqrt((1/length(x))* sum(MD(x, n = round(length(x)/20))^2))\n",
    "    c(NPMD,Burke)\n",
    "})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Based on the values that were generated... we can see that 2nd simulated curve has the highest NPMD and Burke value which is to be expected based on the curve above (red)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above two metrics cover shortcomings of the Sharpe ratio in that:\n",
    "- Denominator penalizes only large gains and losses\n",
    "- Maxima nad Minima are non-parametric measurements thus does not rely on parametric assumptions of normality\n",
    "- Both numerator and denominator standardize against 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The shortcomings of the MD based performance metrics are:\n",
    "- The MD metrics over-value strategies that have low MD which may occur in the future. \n",
    "- MD strongly penalizes high-variance strategies compared to low-variance strategies (as the Burke metric aggregates all $n$ MD's as a variance measure). In our case the 2nd simulated curve has way more variance compared to the first and the profit margin may be more than 3 times greater (e.g. maybe 5x) but based on the Burke value we only see a 3x better performance of that strategy."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Partial Moment Ratios"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Partial moment ratios are based on the concept of semi-variance, or the variance of observations that are above or below the mean (i.e. lower semi-variance or upper semi-variance). The partial moments are based on *max* function where the argument will be based on the difference between $R_b$ and $R_t$ and 0. The equation to get the lower and upper partial moments are as such:\n",
    "$$ \\text{LPM}_n(R_b) = \\frac{1}{T}\\sum_{t=1}^T max[R_b - R_t, 0]^n$$\n",
    "$$ \\text{HPM}_n(R_b) = \\frac{1}{T}\\sum_{t=1}^T max[R_t - R_b, 0]^n$$\n",
    "The $\\text{LPM}_n(R_b)$ ignores those differences that are above $R_b$ and the $\\text{HPM}_n(R_b)$ ignores differences that are below $R_b$. Below is the R code."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%R\n",
    "PM <- function(Rt, upper= FALSE, n = 2, Rb = 0){\n",
    "    if(n != 0){\n",
    "        if(!upper) return(mean(pmax(Rb - Rt, 0, na.rm = TRUE)^n))\n",
    "        if(upper) return(mean(pmax(Rt-Rb,0,na.rm = TRUE)^n))\n",
    "    } else {\n",
    "        if(!upper) return(mean(Rb >= Rt))\n",
    "        if(upper) return(mean(Rt > Rb))\n",
    "    }\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- n = 1, we get the 1st partial moment which is the mean of the returns in excess of $R_b$ or less than $R_b$ for the HPM and LPM.\n",
    "- n = 2 we get the 2nd partial moment (i.e. the semi-variance) assuming a mean $R_b$\n",
    "- n = 3 is the 3rd partial moment (i.e. the semi-skewness) assuming a mean $R_b$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The two important partial moment ratios are Generalized Omega:\n",
    "$$\\Omega_n(R_b) =  \\frac{\\bar{R} - R_b}{(\\text{LPM}_n(R_b))^\\frac{1}{n}}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and the Upside Potential Ratio:\n",
    "$$\\text{UPR}_{n_1,n_2}(R_b) = \\frac{\\text{HPM}_{n_1}(R_b)^\\frac{1}{n_1}}{\\text{LPM}_{n_2}(R_b)^\\frac{1}{n_2}}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Generalized Omega $\\Omega_2(0)$ is the Improved High-Frequency Sharpe Ratio which utilizes the LPM. It specifically utilizes the (see denominator) $\\text{LPM}_2(0)$ which is equivalent to the semi-variance (as n = 2) assuming mean 0 return."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The general gist of the UPR is a measure of the ratio of positive volatility to the negative volatility as is indicated in the equation. The equation represents the ratio of the HPM and LPM's partial moments based on the assumed return $(R_b)$ while using two degree parameters $(n_1,n_2)$ that represents the degree of the moment based on the above or below mean observations (i.e. partial moments described above)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The advantages of the UPR measure is that 1. is able to favor strategies that are able to short a market crash rather than avoid it (as volatility towards market crash can be assessed using the UPR) and 2. The ratio can be used for multiple checks on the degree of the moments."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "          [,1]      [,2]      [,3]\n",
       "[1,] 0.2069097 0.1238478 0.1932985\n",
       "[2,] 2.8118970 2.1091423 1.8469374\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%R\n",
    "\n",
    "# Need to set aside the original benchmark return if CIX\n",
    "Rb2 <- Rb\n",
    "\n",
    "sapply(list(Rb2, Rt, Rt2), function(x) {\n",
    "    Omega <- mean(x, na.rm = TRUE) / PM(x)^0.5\n",
    "    UPR <- PM(x, upper = TRUE)^0.5 / PM(x)^0.5\n",
    "    c(Omega,UPR)\n",
    "})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Based on the smaller volatility of the benchmark, UPR value is greatest for the benchmark then the 1st simulation. Given the high volatility of the 2nd simulation curve the result shows the lowest UPR value for the most profitable curve. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Regression Based Performance Metrics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The regression based model will try to maximize risk-adjusted return with the characteristics of low volatility (low variance), long-term consistency (again low variance and linearity), and high returns (through linear fit). Let's look at the regression equation:\n",
    "$$ R_t = \\alpha + \\beta R_{t,b} + \\epsilon_t$$\n",
    "$\\alpha$ above is termed Jensen's $\\alpha$ and $R_{t,b}$ is the return of a benchmark at time $t$. $\\alpha$ is the intercept term and in terms of the interpretation, provides a baseline value of the portfolio. The $\\beta$ coefficient is basically the measure of volatility-scaled correlation between assets. Below is the regression plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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NXRuTKlGDFgZFHCyKOFg6FXFkZGDQIEyahNDQ2mxGUhEHzeIQBs3iYNEsDpbu\nzOK4exdjx2LFCnh41HJLFHEQ3lHEwaKIg6Ujh/OnTyMkBBERte/O0Jkx0Qw1aGFQxMGiiIOlCxFH\nQgLmzkViIlxd62R7FHEQ3lHEwaKIg1XvI47167F3L5KSYGZWV5ukiIPwjiIOFkUcrHp8OM9Ndj51\nCjExddidUa/HpPqoQQuDIg4WRRys+hpxlJRg9GgAWL++ZpOdq0ARB+EdRRwsijhY9TLiyM9HYCB8\nfTFhAh+bp4iD8I4iDhZFHKz6dzifng5vb0ydylN3Rn0ck1qgBi0MijhYFHGw6lnEcf06hg7FihV4\n/33+dkIRB+EdRRwsijhY9SniOHUKn36KmBg4O/O6H4o4CO8o4mBRxMGqN4fzcXH4v/9DbCzf3Rn1\naEzqAjVoYVDEwaKIg1U/Io6VK/Hzz0hKglaOgSjiILyjiINFEQdL7BGHSoWFC5GdjW3boKelT3sU\ncRDeUcTBooiDJerD+ZISjBoFACtXaq07Q+RjUteoQQuDIg4WRRws8UYceXn44AN4e9dmZeea7pki\nDsIzijhYFHGwRBpxPHkCf3989hnee0/7O6eIg/COIg4WRRwsMR7OX7uGYcPw44+CdGeIc0x4Qw1a\nGBRxsCjiYIku4jhyBKGh2LYN7u5ClUARB+EdRRwsijhY4oo4du7E6tVITIS1tYBVUMRBeEcRB4si\nDpaIDufDwxEdjd27he3OENWY8I8atDAo4mBRxMESRcShUmHOHKSmIiYGpqYCFyOxiIMatDBMTU1N\nRfC3Lio2NjbGxsZCVyEuTk5OMplMyAqKixEcDGtrhIdrc7JzFSjiILyjiINFEQdL4MP5nBz4+GDI\nEHz6qZBlvIoiDsI7ijhYFHGwhIw4Hj/G0KGYPx8BAcIUUAlJRRw0i0MYNIuDRbM4WILN4khOxoQJ\nWLcObm7CFFA5ijgI7yjiYFHEwRLmcP7QIUyejO3bRdidQREH0QKKOFgUcbAEiDi2bMF33yEpCU2b\nanW/GqOIg/COIg4WRRwsbUcc4eH44w/Ex8PERKv7rQ6KOAjvKOJgUcTB0t7hvEKB6dORmoqtW8Xc\nnUERB9ECijhYFHGwtBRxFBcjJARt2ohnsnMVKOIgvKOIg0URB0sbEUd2Nvz9MXEiRo7kfV91gSIO\nwjuKOFgUcbB4P5y/fx+DB2PBgvrSnUERB7ONSCkAACAASURBVNECijhYFHGw+I04rl5FSAgiIvDO\nO3ztggcUcRDeUcTBooiDxWPEcfAgwsIQHY36lhhQxEF4RxEHiyIOFl+H85s24YcfsGdPvevOoIiD\naAFFHCyKOFi8RBzh4Th0CImJsLCo4y1rBUUchHcUcbAo4mDVccShUGDGDBgaIjISwq5iWgsUcRDe\nUcTBooiDVZeH8y9fYvhwtG+P8PD6251BEQfRAoo4WBRxsOos4sjOxpAhCA7G1Kl1sDVBUcRBeEcR\nB4siDlbdRBz37iE4GN99h1696mBrQqOIg/COIg4WRRysOjicP3sWQUGIjNSN7gyKOIgWUMTBooiD\nVduI48ABzJmD+Hi0bl13RQmMIg7CO4o4WBRxsGoVcWzciG3bEB9fT6fTVYYiDsI7ijhYFHGwan44\nv2QJjh5FQoKOdWdQxEG0gCIOFkUcrJpEHAoFJk9GTg4iImBoyE9dQpJUxEENWhimpqampqZCVyEu\nNjY2xsbGQlchLk5OTrJqzVkuKMCwYXB3x+LF9XqycxUo4iC8o4iDRREHq3qH81lZ8PPDxImYPJm3\nioRHEQfhHUUcLIo4WNWIOFJTMXgwFi7E4ME8FyUwSUUcNItDGDSLg0WzOFiazuI4cwYzZ2LTJrRq\nxXNFwqOIg/COIg4WRRwsjQ7nExPx6adITJRCdwZFHEQLKOJgUcTBen3EERGB//4Xu3bBzk5bRQmM\nIg7CO4o4WBRxsKqKOFQqLFyItDTEx8NAQm9kijgI7yjiYFHEwar0cF4ux6RJALBhg6S6MyjiIFpA\nEQeLIg6W+ogjPx/DhqFrV4SFCVCT0CjiILyjiINFEQdLTcSRkQF/f8yZA29vISoSHkUchHcUcbAo\n4mBVPJy/cwcjRmDZMsl2Z1DEQbSAIg4WRRysVyKOU6cwahQiI+HhIWhRApNUxKGlBq1SqXJycsqn\naSqVKjc3Vzt7FyFai4NFa3Gw/lmLIz4e8+YhMREtWwpdlMAo4qhj169fb9eunbW1tYuLS2xsLHdn\ncXGxlZWVFvYuThRxsCjiYP11OL9qFTZtQlISbG2Frkh4FHHUsSlTpowdO7aoqGj9+vVTp049fvy4\nFnYqchRxsCjiYOXn5am++AKXLmHbNpiZCV2OKFDEUccuX77873//28jIqF+/fmvWrJk4cWJJSclr\nX7Vz584BjNjYWD8/P4VCUVRUdP/+/fp7Iz8/39jYWPAyRHXD3Nw8PT1d8DLEc+PB7duOc+cqFIr7\nn32mkMkEr0ckN+RyuRjKKLsxdOhQ/pqnrG4u6l6lli1bbtq06e233wagUqmGDx9ub2//ww8/mJqa\nVnfvs2bNSk9Pj46O5qdS7dm8eXNubu6MGTOELkRECgoKjI2NDSR22kWl8vMRFPRy8GCz0FChSxGX\nFy9eWFpaCl3FPyZMmDBv3jwXFxc+Nq6NT9Dffvutl5dXv379srKyZDLZ//73vzNnzvTs2VMLuxYt\nijhYFHH8Iz0d3t6YOjVn0CAtfISqXyQVcWjj08qIESN69ux5+vRp7jv6xo0bnzhxIiEh4dy5c1rY\nuzjRiSosOlHlL9evY9w4rFmDTp1qcclYnSWpWRxaOpx0dHQsn9QYGRmNGDFixIgR2tm7CNEsDhZF\nHABw8iTmzEFMDJydIb7DeTGQ1JjQiSrCoIiDRREH4uIwfz5iY7nujJpdNFbXUcRBeEcRB0vqEUd4\nOI4dQ1ISyp3BpOkVVaREuhHHzZs3K3temzZt+C9GQijiYEk34uBWds7JwbZt0HvloFZSh/MaktSY\nvPJm+Oijj/bv329iYsL+/hkZGVqsSvdRxMEqLCw0MDCQXIMuKcGHH8LVFeHh7IP5+fkWFhZ/ne1N\nAAB5eXkSbdC//vrrpEmTZDLZ2rVrhSpIIijiYEkx4sjNhb8/xoxBUJDaxyniYEkq4qj4JWFgYGCL\nFi0EKUVSKOJgSW4tjidP4OODf/+7su4Mia07oSFJjUnFw8k+ffr06dNHiEqkhSIOlrQijmvXMH48\n1q6Fu3sVz6KIgyXdiINoDUUcLAlFHIcP47PPsG0bmjWr+okUcbAkHXEQ7aCIgyWViGPnTnz3HZKS\nXtudIbHDeQ1JakyoQQuDIg6WJE5UCQ9HdDTi4tCokSZPpxNVWJI6UUV9g05JSVGpVCUlJTt37oyI\niNBkdVBSLXRFFZaOX1FFpcKnnyI1FTExMDHR8EX/XFGF/E3qEcfnn3/eqVMnhUKxbNmyzz//fN26\nddOnT9d+ZbqNIg6WLkccxcUICoKNDcLDK5yKUjVJHc5rSFJjouZvZfXq1cnJyfr6+qtWrYqIiNi3\nb198fLz2K9NtFHGwdDbiyMmBjw98ffHpp9V9KUUcLElFHGpmcahUqkaNGp0/f16hUHTt2vXly5cU\ncdQ5msXB0s1ZHI8fIzgYixahd+8avJpmcbAkFXGoadDDhw/v27dvfn7+rFmzsrKyhgwZ0qtXL+1X\nptso4mDp4FocycmYMAHr1sHNrWYbkNS6ExqS1JioeTOsXr06Li5OLpcPHz782bNnfn5+U6ZM0X5l\nuo0iDpaunahy6BAWLMD27WjatMbboBNVWFI/UcXAwGDEiBFKpTI7O9vBwWHu3LnaL0vnUcTB0qmI\nY/Nm/PwzkpJQu1ZCEQdLUhGHmi8J09LS+vXrZ2Fh0adPn5SUlF69eqWmpmq/Mt1GEQdLd2ZxhIdj\n927Ex9eyO0NiMxY0JKkxUdOgP/nkE09Pz6ysLACurq7e3t6hdF3hukYRB0sXZnEoFJg+Hamp2LpV\n88nOVaBZHCxJzeJQ06B///33L7/8kjtlQF9ff/bs2RcuXNB6YTqOTlRh1fsTVYqLERKCt96q7mTn\nKtCJKiypRxx2dnanT58u+/Hq1av29vZaLEkSKOJg1e+IIzsbgwdj6FBMm1aHW5XU4byGJDUmar4k\nXLFihZ+f34ABAzIyMj788MNdu3ZFRERovzLdRhEHqx7P4rh3D8HBWLIE77xTtxumWRwsqc/i6N+/\n//Xr13ft2tW6desmTZosXLiwmQbLbpFqoVkcrPo6i+PKFUydiogI8HDdTprFwZJUxKH+04qdnd34\n8eO1XIqkUMTBqpcnqhw8iLAwxMSAn04qqZMyNCSpMXnlzWBubr537161p6UkJydrqyRJoIiDVf8i\njk2bsHUr9uyBhQVPe6CIgyXdiGPHjh3t2rWLjo4WqhrpoIiDVc8ijiVLcOMGEhNhaMjfTijiYEk3\n4vDy8nry5Mnw4cPPnTtnbm4uVE1SQBEHq95EHNxkZyMjREaC58+2kjqc15CkxqTiNDsHBwd3d/dV\nq1YplUpBCpIIijhY9eNElZcv8cEH6NgR4eF8d2fQiSrqSOpElYqfVmQyWXp6elxc3NKlS+3s7PT+\nnm9PGXTdooiDVQ8ijqwsBAZixgz4+GhnhxRxsKQbcXB++ukn7dchNRRxsMQecXCTnb//Hj17am2f\nkjqc15CkxkTNm6F9+/YAuNXsrK2t6RtkPlDEwRL1LI6zZzFzJjZuROvW2twtzeJgSWoWB61mJwxa\ni4Ml3rU49u/HnDmIj9dydwatxaGOpCIOWs1OGBRxsES6FsfGjQgPR0ICmjTR/s4lte6EhiQ1JrSa\nnTAo4mCJcRbHkiU4ehTx8WjYUJD90ywOlqRmcdBqdsKgiIMlrohDocCkScjJQWQkr6eiVI0iDpbU\nIw5uNbvAwEBuNbuBAwcuXrxY+5XpNoo4WCKKOAoKMGwYOneG0H/5kjqc15CkxoRWsxMGRRwssczi\nyMzEyJH49FMMGiRwJTSLQx1JzeKo+GZQqVR5eXncana3bt06efJkUVGRIJXpNjpRhSWKE1Xu3kVI\nCH74AW+/LXQpAJ2ooo50I467d++6ubkFBQUBePDgQefOndevX//2228fPHhQoPJ0FkUcLOEjjjNn\nEBKCTZtE0p0hscN5DUlqTF5p0J988snw4cMTEhIAhIWFzZgx49ixY1u2bFm4cKFA5eksijhYAs/i\nSEzEnDlISICrq2A1MGgWB0tSszheiTj++OOPbdu26evrK5XKpKSk3bt3A+jXr19gYKBA5eksijhY\nQkYcERFISkJSEszMBKtBHYo4WNKNOFQqFbc60oULF0pLSz08PAAUFRXRdxR1jiIOljARh0qFsDCc\nOIGYGLF1Z0jscF5DkhqTVxp0165dly1bVlBQ8P333w8ZMkRfXx9AVFQU16lJHaKIgyVAxCGXY9Ik\nANiwAYLPHlGHIg6WdCOO5cuXDx48eO7cuU5OTseOHSsqKho8ePDFixf37dsnVH26iiIOlrYjjvx8\nBAXBxwcTJ2p1v9VBEQdLUhHHKw26TZs2t27devz4sZOTk56eXklJycSJE/v06dNEiFUIdBtFHCyt\nLjeakYGRIzFvHt5/Xxu7qylJLa2pIUmNScUzCfX09Jo2bcol0UZGRv7+/tSd+UARB0t7EcedOxgx\nAsuXi7w7gyIOdaQbcRCtoYiDpaWI49QpzJqFzZvRsqU2dlc7FHGwJBVxqFmLg2gBRRwsbcziiI/H\nvHlITKwX3RkSm7GgIUmNCTVoYVDEweI94vjxR2zejD17YGvL417qFEUcLKlHHPv27Vu4cGH5Uejb\nt++PP/6oxap0H0UcLB4jDpUKCxfi8WPExIhzOl1lKOJgSSriUPPHOnXq1C+++MLT07Ps/BQ6UaXO\nUcTB4msWR0kJxo+Hiwv+97863jL/JDVjQUOSGhM1b4YOHTqMGTNG+6VICkUcLF6WG+UmO/v7Izi4\nLjerLbTcKEtSy42qyaB79uy5f/9+7ZciKXRFFVbdX1ElPR3e3pg6tZ52Z9AVVdSResSRlJT0+eef\nN27cuHHjxmV/HMnJydotTMdRxMGq44jj+nWMG4c1a9CpU91sUAiSOpzXkKTGRM2b4aefftJ+HVJD\nEQerLiOOkycxZw62bUM9vxgQRRwsSUUcFd8MT548GT58+Llz58zNzQUpSCJoFgerzmZxxMZi1SrE\nxkIMl2ipHZrFwZJUxFExg3ZwcHB3d1+1apVSqRSkIImgiINVNyeqhIfjl1+QlPS/uDiZTBYWFlYH\nlQlHUidlaEhSY1LxE7RMJktPT4+Li1u6dKmdnR23KAcog65rFHGwahtxqFSYNw+Fhdi2DXp6v//+\nO4A//vijLkvUOoo4WJKOOEAZtFZQxMGqVcRRXIxx4+DqisWLuTu+//77rl27Dh48uG6KEwhFHCxJ\nRRxqGnT79u21X4fUUMTBqvksjtxcjByJDz9EuWuz2dvbz5w5sy7rE4KkZixoSFJjoubN0KtXrwr3\ntGjRYvPmzVqpRyoo4mDVMOJ48gRBQQgLQ58+vJQlKIo4WFKPOJYuXcrdUKlU6enpq1evHjRokHar\n0n0UcbBqEnEkJ2PCBKxdC3d3HioSHkUcLKlHHN27dy//o5eXV+/evQMCArRVkiRQxMGqdsRx+DA+\n+0wHJjtXQVKH8xqS1Ji8frnRZ8+e3blzRwulSApFHKzqLTe6Ywe+/x5JSTrcnUHLjaoj9eVGy2fQ\nCoXi0qVLo0eP1mJJkkARB6saEUd4OE6cQGwsTEz4rEh4FHGwpB5xLFy4sPyaNRYWFq6urlosSRIo\n4mBpFHGoVJgzB8XFiI6Gnu5fbkJSh/MaktSYqHkzfPTRR+VPSykqKmrZsuWjR4+0WJXuo4iD9fpZ\nHMXFGDsWnTtj9mwt1iUkmsXBku4sDu69oVAoKrxJhgwZotWiJIAiDtZrIo6cHIwcifHjIaXvqyni\nYEk34uA+0/n4+OzatUugeqSCIg5WVRHH/fsIDsa336J3b63XJSRJHc5rSFJjoibF47qzUql8/vw5\nfYPME4o4WJXO4rh6FQEBWLNGat0ZNItDHUnN4lDToNPS0vr162dhYdGnT5+UlJRevXqlpqZqvzLd\nRldUYam/ospvv2HKFOzYgY4dhShKYHRFFZakIg41DfqTTz7x9PTMysoC4Orq6u3tHRoaqvXCdBxF\nHCw1y41u3oylS5GUBCm9J8uT1NKaGpLUmKhp0L///vuXX37JfZbR19efPXv2hQsXtF6YjqOIg1Ux\n4ggPx8GDSEiAZAJHFkUcLKlHHHZ2dqdPny778erVq/b29losSRIo4mD9E3EoFJg2DampiIyEkZHQ\ndQmJIg6W1COOFStW+Pn5BQYGZmRkfPjhhwMHDlz89xq7pK5QxMH6K+IoLkZICNq2RXi4FE5FqZqk\nDuc1JKkxUTOlqX///tevX9+1a1fr1q2bNGmycOHCZjq93IEgKOJgFRYWGvz5p8GoUQgNxciRQpcj\nCnSiCktSJ6qo/4RiZ2c3fvz4sLCwKVOmNGvW7M8//6zNPm5WropXXbt27b+Mq1evtmnTRqVSyeXy\nnJyc+ntDqVSamJgIXoaobljl5ur7+qq++EI+bJgY6hHDDUdHR4VCIXgZorrRoEEDMZRRdqNdu3a1\naY9Ve+UT9JMnT+bPn5+Wlubn5zdt2rSoqKgrV66kpaUdPXr06dOnNd7HRx99tH//fhMTE/b/vYyM\njBpvtl5TKBT0CfoVV65g8uT8lSstu3WD5mva6boXL16Ym5sLXYW4FBYWNmrUSOgqtERW/jvi999/\nXyaT+fn5xcfHl5aWPnnyxM/Pr3Hjxq6urrU823vSpEkymWzt2rW1LHfWrFnp6enR0dG13I7gIiMj\nc3NzZ82aJXQh4nDwIMLCstesadCqlZqp0BL2+PFjR0dHijjKe/Tokai+J5wwYcK8efNcXFz42Pgr\nn6CPHTv24MEDa2vr/v37t2zZ8ubNm61bt66T3QQGBpafGUJoLY5/REUhJgZ79jS2sBC6FNGhtThY\nourOfHulQRcWFlpbWwNwcXExMjKqq+4MoE+fPn108ZJxNUazOP6yZAlu3EBCAgwNa37RWN0lqXUn\nNCSpMXnlS8LyR1J0VMUruVwu9QxaocCUKXjyBJGRMDREda+oIg10ogpLUieqvPJpRaVSnTp1irut\nVCrLboO5UCGpJalHHAUFCA7Ge+9hypSy+2py0VhdRxEHS7oRh4ODw/Dhw7nbdnZ2ZbcB0IL9dUvS\nEUdWFgIDMWMGfHzK300RB0tSh/MaktSYvPJmoC6sNdKNOFJTERyMpUvRs2eFR15/RRXpoRNVWJI6\nUYXeDMKQaMRx9ixmzsTGjVD3/TNFHCyKOFiSijikvtaBUKQYcezfj7lzkZCgtjtD7XKjkiepdSc0\nJKkxoQYtDMlFHJGRCA9HfDzs7Cp7Cs3iYNEsDpZ0Z3EQrZFQxKFSYeFCPHyI+HhuOl1lKOJgUcTB\nooiD8E4qEYdCgcmTUVSEiIiquzMo4lBHUofzGpLUmFCDFoYkIo6CAgwbhs6dodl64hRxsCjiYFHE\nQXin+xFHRgb8/fHppxg0SMNXUMTBooiDRREH4Z2ORxx372LECPzwg+bdGRRxqCOpw3kNSWpMqEEL\nQ5cjjtOnERKCiAh06VKt11HEwaKIg0URB+GdzkYcCQlYsQKJibC1re5LKeJgUcTBooiD8E43I44N\nG7BpE5KSatCdQRGHOpI6nNeQpMaEGrQwdC3iUKkQFoY//kBMDMzMarYNijhYFHGwJBVxUIMWhqmp\nqampqdBV1BG5HKGhALBhA2qx1JGNjQ1d76oCJycnWimpAoo4CO90J+LIz8fQofD0RFhYLbdEEQdL\nUofzGpLUmFCDFoaORBzp6fD2xtSpmDix9hujiINFEQdLUhEHzeIQhi7M4rhxAx9+iNWr0blznWyP\nZnGwaBYHiyIOwrt6H3GcOoVx47BlS111Z1DEoY6kDuc1JKkxoQYtjPodccTH4//+D4mJaNmyDrdK\nEQeLIg4WRRyEd/U44vjxRxw5gqQk1PUsFIo4WBRxsCjiILyrlxEHN9n51i1s317n3RkUcagjqcN5\nDUlqTKhBC6P+RRwlJRg1CgB+/BF6vPzZUMTBooiDRREH4V09izjy8hAcDH9/BAfztxOKOFgUcbAo\n4iC8q08RR9lkZz67MyjiUEdSh/MaktSYUIMWRr2JOK5dw9ChWLkSXl5874oiDhZFHCyKOAjv6kfE\n8ccfmDsX27ahWTMt7I0iDhZFHCyKOAjv6kHEERuLzz5DbKx2ujMo4lBHUofzGpLUmFCDFobYI47w\ncGzdiqQkaPFTLUUcLIo4WBRxEN6JJOJ48OCBg4ODkZHRP3epVJg7F0VFiInhaTpdZSjiYFHEwaKI\ng/BODBFHZGRk8+bNvcp/+1dcjJAQmJoiPFzL3RkUcagjqcN5DUlqTKhBC0MMEUdBQQGAkpKSv37O\nyYGPDwYPrv3KzjVDEQeLIg4WRRyEd2KIOKZNm+bp6dm6dWsAePIEQUFYuBDvvitUPRRxsCjiYFHE\nQXgnhohDJpN5enpaWloiORnDhiE8XMDuDIo41JHU4byGJDUm1KCFIYaI4y+HD2PSJGzfDjc3YQuh\niINFEQeLIg7COzFEHACwYwciIrBnDywthS6FIg41KOJgUcRBeCeGiAPh4di2DbGxYujOoIhDHUkd\nzmtIUmNCDVoYAkccCgWmT0dqKqKjYWIiWBmvooiDRREHS1IRBzVoYZiamprysOa9RrjJzs7Ogkx2\nroKNjY2xsbHQVYiLk5OTTCYTugpxoYiD8E6wiCMnB4MHw88Ps2cLsPcqUcTBktThvIYkNSbUoIWh\nhYgjICBAJpOdOnXqn7vu38egQfj8c/j787rrmqGIg0URB4siDsI7viOOY8eOxcTEADh37txfd129\nipAQbNiA3r35229tUMTBooiDRREH4R3fEceCBQsAeHh4jB8/HgB++w1TpiA6Gm+9xd9Oa4kiDpak\nDuc1JKkxoXnQwuA74hg1apSent6sWbNMTU2xadNfa4eKYzpdZQoLCw0MDAwM6G/yH/n5+RYWFvQh\nury8vDxLcf8l1yF6MwiD7xNVxo0bN27cOAAID8eFC0hIQPk1RUWJTlRh0YkqLIo4CO9qE3Fo2tkV\nCkybhtRUREaKvzuDIg51JHU4ryFJjQk1aGHUOOKIiIgwMTHhkmW5XD58+PB+/frdvXu34vOKihAc\njHbtxDbZuQo0i4NFszhYkprFQRGHMGoccdy4cQMA15FzcnJ27twJ4Ny5cy4uLv88KTsbI0di0iSM\nGFE35WoFRRwsijhYkoo4qEELg404ioqKTDQ46zosLMzDw6NXr14AbG1t4+LiHj58OGzYsH+ece8e\ngoPx3Xfo1auuq+ZXQUGBsbExfUlY3osXL6TzhZiGJDUm9ePgV/dUiDgWLVpkamo6f/78176wQYMG\nAQEBZR8i/Pz8Zs6caWho+NfD584hMBAREfWuO4MiDnUo4mBRxEF4VyHiuHbtGoDr16/XaqMHDmDR\nIuzcifp5XEwRB4siDpakIg76BC2MChHHmjVrtm7dun79es238OTJkwkTJqxbt+6vnzduxPLlSEqq\np90ZNItDHUnNWNCQpMaEGrQwKkQcjRs3DggIsLa25n5ctWrVF198UVxcrFKpXrx48fvvvwcGBh4+\nfBhAfn4+95zo6OgNGzZMnjxZLpdjyRIcOYKEBFhYaP93qSsUcbAo4mBRxEF4V8Usjjt37syYMQOA\nh4fHunXr9uzZ07lz5wsXLmRlZa1atSo2Nnbbtm0jRozw9fU9duxY186dDWbMgKUlIiNRz883o4iD\nRREHS1IRBzVoYaSkpOzbt0+hUEybNq3CQ87OziEhIXl5eT169PD19QXQtWtXBweHqVOnDho0CH/P\nsXNxcYnbsgXBwfDywuTJ2v8V6hzN4mBJasaChiQ1JvRmEMbNmzfz8vKmT58eGhr64MGDM2fOPHjw\n4MMPP7S3tzc0NNy8eTP3tIcPH169enXgwIFc27p///7Fixe9vb0BICsLgYGYORODBwv4i9QhWouD\nRWtxsGgtDsI7T0/Px48fu7m5GZU7CfvRo0c//fRT+afdvHlz69atNjY2np6eAJydnZ2dnQEgNRXB\nwfjhB7z9tnYL5xFFHCyKOFiSijjoS0Jh2NjYDBky5PLly+XvfO+99yo87euvv96yZcv333//yr1n\nzyIoCFFRutSdQbM41JHUjAUNSWpM6BO0tmVnZ69cuVIul5uZmX333XdNmjR58OBBq1at/P39jx49\nOnbsWH19/Y8//tjBwcHGxmbatGkNGjSYMmXKP6/fvx9LliAxEXZ2wv0SvKCIg0URB4siDsKjDRs2\nLFy4EICzs/ODBw/eeeedY8eOASguLh4zZgz3nPPnz1++fNnf3z86Ovr8+fPffvutjY1Nx44dERmJ\nHTsQH4+GDYX8HfhBEQeLIg4WRRyER/379wdgZ2dnYWEBgOvOAFauXNmvXz/utqOjI4Dnz58nJSUt\nWbLk4MGDv/z8M8LCcOwY152VSqVA5fOIIg6WpA7nNSSpMaEGrW2dO3c+cOBA+/bty3o0p6io6NCh\nQ9ztTp06zZgxo3379oMHDwZgAMxJTUVRESIiYGh48eJFfX19b29vHTutg05UYdGJKiw6UYXw61//\n+teAAQMq3Mktx8H55ptvym43AHYYGloNGIDQUO4ebsmOvXv3FhQUWNTnUwcroIiDRREHS1IRBzVo\nbUtLS/v222/t7Oz09PQyMjKqfrI9EANstrHx+rs7A/D391cqlS4uLrrUnUEnqqgjqZMyNCSpMaGI\nQ9vCwsLWrFljZWVVtvIGKykpCYALEG9o+L2Dw/Nu3Z4/f172qIGBwahRo97WrTl2oIhDHYo4WBRx\nEF7ExsaWnYeSkpJS4VFHR0dzc3MvL6+TJ09+9tln3YAVwKjS0tvp6YiPv3PnTv/+/VesWKH1qrWH\nIg4WRRwsijhIHUtNTZ03b97169eTk5M7d+4MgI04njx5AuDWrVsAfIH/GBgMkcuN33ijnaWlsbHx\nhQsXkpOTly9fDuD48eP29vaurq4C/TZ8oYiDJanDeQ1Jakwo4tCGmJiYbdu2JScnT5gw4f79+wCq\niDjGA6OB9+TyZ8CjR49CQ0MPHDiwAbfucQAAGXFJREFUYMGCpKQkmUy2a9eu3r17t2rVSvcmG1HE\nwaKIg0URB6ljXbp0AfDGG2+ULcnPRhwAZMAXwBuAPyAH7Ozsnj592qhRo0aNGnXq1MnOzg6A3d8n\nEBobG2urfC2hiINFEQdLUhEHfYLmXV5eHhdNPHr0qOxOOzs7e3v78k8zAjYBACYA3Nka7u7ujx49\nCgkJSUhIGDp0aNeuXXNycrp3756bm1tSUqLJFWbrFzpRhaV7x0m1J6kxoQbNu6SkpL1791a4s0LE\nYQ7sBI4C6ZMmNWvWzM3NDYCBgcHs2bP19fUzMzMB9O3bt0GDBgAsLS3/uUqsDqGIg0URB4siDlJb\npaWlu3fvbt++fVFRUW5u7tChQxUKRWJiYtkTykccDkAM8C2wFzDdtKmwsPDhw4fBwcFPnz7dunUr\ngD///LOkpMTAwEC3F82hiINFEQdLUhGHVhu0UqnMz883NzfX09PxT+6rV6/++OOPy35csmTJzp07\nyz+hbBbHW0AkMBW4AAAoLCzknvDzzz9zN9q0aTNjxgyd/MhcAc3iYElqxoKGJDUm2miURUVFCxYs\ncHV1NTY2trS0NDIyatmyJXdRVC3sXRDcHDgfH58+ffoAmDNnzpkzZ8o/gYs4ugMRQMjf3Vkmk3Gf\nIjt27Fj2zLVr15qammqvdOFQxMGiiIMlqYhDGw06NDT0ypUrkZGRmZmZJSUlT58+3bx5c0pKymSd\nuJKeWt7e3i9fvkxMTOQuKshKSUlpde3aN4APcOfvO0NCQr744ot27dq1bdu2Xbt2AMaNG/fuu+9q\nq2qB2djY6N7UlFpycnLS7VyrBiQVcci08P+zjY1NWlpahY+Bcrn8zTfffPjwYWWv2rlz59q1ayvc\neffuXSsrKysrK5VKVVxcbGJiIsIbBQUFz58/d3R0VCqVBgYGV65csbe3v3XrlrGxsbOzM3fjP0ZG\nnfLyJhgb2/19j7Ozc1FR0Z9//mlnZ3fr1i0HBwcnJyfuW0GR/F5835DL5XK5XPAyRHXDwMBAX19f\n8DJEdaOoqMjU1FTwMspu5Obmbty4sUOHDnw0T6j417Fjx7i4uAp3Hj582N3dvbqbiomJ+emnn+qo\nLr5wA+vq6jpu3LiSkpIvv/yy/IDLgDBgs5VVh3btqvh3+eGHH4T+PbTt2bNnRUVFQlchLo8ePVIq\nlUJXIS5paWlCl/CK8ePH37lzh6eNa+MLmf/973++vr6ff/5527ZtGzZsmJ+fn5KSkpmZmZCQoIW9\na9/8+fO//vrr27dv3759OzMz89133+3bt+/hw4cBGAERwB1gVE4OcnKq2EhQUJC26hULmsXBolkc\nLElFHNpo0J6eng8fPjxy5Mi9e/dycnKsrKzGjx/fp08fXZ2Z8NVXX/Xu3Zu7AmxSUtKZM2eePXsG\noCHwMxAN/KJuLY4y+/fv79Gjh7m5ubbrFhrN4mBJasaChiQ1Jlp6MxgaGrJL1OuwAQMGREREpKWl\nrV+/Pj8/H4AjEAN8BfwKALCysjIwMGAb9OPHj7nrXUkQXTSWRReNZUnqorE6Ph9Za1QqVceOHWUy\nWVRUFIAzZ848efKkS5cuaWlpOTk57YBYYMbf3RlASkpK+UuolBk6dOgnn3yixcJFhGZxsGgWB4si\nDlJtRUVFV69eBTB27FgPD4/u3buXPdQH+BoYCZSfsFJZxHHmzJkzZ86EhYXp2NVSNEERB0tSh/Ma\nktSY0Cfoart+/frIkSMjIiK4H1UqVXp6+pEjR4YPH87dk5+fX/Yp+ANggUw25NXuDGYtjtmzZ6en\np588eXLmzJlr166VYHcGnaiiDp2owpLUiSramGZXh8Qwze7TTz8tP3SBgYFlg7l9+3YAvXr1unz5\n8osXL/7brt12wBQwMjKq+l/hm2++EfaXIoTUTL2fZqdjxowZk5qa6u3tzf2Ym5tb9hB3Ms7x48fd\n3dx+btq0MC1tMqAEUFJSYSMVIg7KGUERhzqSOpzXkKTGhN4M1da2bVvukzJn69atJ06cuH79+s6d\nO/39/QEYA5FAjkz2EQDA1taWm2ZXXoVZHNx1sCSOZnGwaBYHi2ZxEE1dunRp3759AwcO9PT0PHXq\nVEFBgRXwm5mZy6xZgZcuPXr0aPz48WrPNagwi6Np06ZarFqkaBYHi2ZxsCQ1i4MadM2VlJR06tQp\nICBg06ZNpqam7du3HzNgwKUWLea/fNlt+XIAz58/37Bhw6VLl8zMzCq8lruiioGBQatWrdasWfPW\nW28J8RuIC11RhSWpq4doSFJjQoeTNWdoaOjl5bVv3742bdosWrQIyclTkpNfbN58dNQoAF9++WXZ\nucsuLi4zZ848dOiQq6vrokWL8HfE8ezZM7UXJ5QmijhYFHGwJBVx0Juh2goLC3fs2OHh4dG2bdu9\ne/eWlpYaGho2vX17LrCiZ8+tISFP33vv0KFDAQEBAKZNm7Z9+/arV6/Gxsbu2bNHpVKtX7/+yZMn\nXF8ODQ0V+rcREVqLg0VrcbAkFXFQg6628PDwefPmAVCpVAAMDQ33jh8fnJ4ePnBg2PLlAGxtbfv2\n7evr62tra7tixQpfX99Vq1Z99NFHAGQy2e3bt11dXeVyeadOndatWyfs7yIqNIuDJakZCxqS1JjQ\nm6HauIVfAwIC1q1b17x58/du3syPiBgGvJGaWvZ5JyMjo6CgoHnz5gYGBnp6eomJiTk5OX369NHT\n0zMzM7t169aECRPYYFriKOJgUcTBklTEQV8SaqS0tHT06NG+vr7Pnj0bNGhQaWmpn5/ftMmT73h5\nFV2//jIiogi4c+fO8ePHuecfPHjw4MGD4eHh0dHR//73vwEcO3as7BuwvXv3RkdHR0REVHG9Agmi\nWRwsmsXBooiDVJSWlrZ582YAJ0+eHDJkiIGBgftbb/0MFLZrZ/DTT6P09O7eu5ebm9uvXz/u+R9+\n+GFWVpanp+eKFSsuX77M3Xnz5k3uYoPvvvtu//79TUxMKGEsjyIOlqQO5zUkqTGhN4NG3nzzzR9/\n/PHZs2fcKs/IyWn973+3jo6Gvz/3BG5uRhkrK6uvv/4aQIMGDaytrblLepd9gra1tQ0ODs7NzdXX\n19fmbyFyFHGwKOJgSSrioDeDpqZPn/7Xrfv3ERSEJUvwzjvln1BUVHT58uXWrVtPmjRJJpNt2LCh\nQYMG//rXv/71r389fvy4qKjIxcWl7MmmpqY6fFHzmqFZHCw6xmJJKuKgDLqarl5FSAgiIip0ZwBB\nQUHdu3cPDQ3dtm1bTEwMt/roixcvxo4du2rVKmdn5/JPLi0tLS0t1V7Z9QGdqMKS1EkZGpLUmNAn\n6Or47Td88QWio6Hu/3DuC64WLVosWrRIX1/f09MTwIABA86ePQvAz8+vW7duZU/mrmCtrbrrB4o4\nWBRxsCjiIOps2oStW7FnDypZrPnnn38OCwtr3bp1+TsbN24MoGvXrm5ubuXvp4iDRREHiyIOlqQi\nDmrQmgkPx8WLSExE5Re61dPTq9CdASQmJqamprZp06bC/RRxsGgWB0tSMxY0JKkxoQz6dRQKTJ2K\n1FRERlbRnStjZGTEdmdQxKEOXVGFRVdUYUnqiirUoKv08iWGD3/RtCnCw1GnOaCpqSm3uj8pQyeq\nsOhEFZakIg5q0JXLzsaQIRsKCxv93//Nnj27/CMZGRm7d++uTYhMEQeLZnGwJDVjQUOSGhNq0JW4\ndw+DByMsbL+lJYDMzMzyDwYEBPj4+HCnotQMRRwsijhYFHGwKOKQirt37wYHB//vf/+r+MC5cwgM\nRGQkevWKiIjYv39/hWXnmjRpAqDC1OZqoYiDRREHiyIOFkUcUrF58+Zffvml4qLMBw5g1izs3InW\nrQE0aNBgwIABFZppTExMTk7O+PHja7xrijhYFHGwJHU4ryFJjYmkpzQFBgZevXq1f//+/9y1cSO2\nbUNSUmWTncs0atSoNrumiINFJ6qw6EQVFp2oIhWtW7fmljH6y5IluHkTCQk1mE5XXXSiCotOVGHR\niSosijikR6HA5MnIyUFEhBa6MyjiUIciDpakDuc1JKkxoQYNFBRg2DC4u2Px4rqd7FwFijhYNIuD\nRbM4WJKaxSHpiAMAsrIQGIiZMzF4sDZ3SxEHiyIOFkUcLIo4JCM1lZvsrOXuDIo41KGIgyWpw3kN\nSWpMJNygz5xBUBCiovD229rfOUUcLIo4WBRxsCjikIDERCxbhsRE2NkJsn+KOFgUcbAo4mBRxKHr\nIiKwbh127RKqO4MiDnUo4mBJ6nBeQ5IaE4k1aJUKYWE4cQIJCWjYUMBCKOJgUcTBooiDJamIQ0oN\nWi7H5MkAsGEDhD5djdbiYNFaHCxai4NFEYcuys/HsGHw8EBYmNClABRxqEMRB0tSh/MaktSYSKNB\nZ2Rg0CBMnowK6yIJhyIOFkUcLIo4WJKKOHR2FsetW7e2bt3q7+/fxtAQY8dixQp4eAhd1D9oFgeL\nZnGwaBYHS1IRh8426E8++SQpKSln374VADZtgqur0BW9giIOFl00liWpC6RqSFJjorMRh5+fnx/w\naXY2EhPF1p1BEYc6FHGwKOJgSSri0NkGPQGI++ADx4sXYWsrdC1q0CwOFs3iYNEsDpakIg5dbNDc\nZOdTpxAdDTMzoatRjyIOFs3iYElqxoKGJDUmOtegS0owejQArF8v+GTnKlDEwaKIg0URB0tSEYd4\nW1hN5OcjMBC+vpgwQehSXoNmcbBoFgeLZnGwKOKon9LT4e2NadPE351BEYc6FHGwJHU4ryFJjYmu\nNOjr1zF0KFasgJeX0KVohCIOFkUcLIo4WBRx1DcnT2LOHMTEwNlZ6FI0RREHiyIOFkUcLIo46pW4\nOMyfj9jYetSdQRGHOhRxsCR1OK8hSY1JPW/QK1fi55+RlIT69uGLIg4WRRwsijhYFHHUByoVFi5E\ndja2bYNe/ftvhiIOFkUcLIo4WBRxiF5JCUJCAGDlyvrYnUERhzoUcbAkdTivIUmNiax+HUD9+uuv\nX/3nPyvS0/c7OByytxe6nJqTy+UvX768c+eO0IWIyIgRI06fPv3w4UOhCxGRTz75ZOXKlfT/Vnlz\n587dv3+/0FX8Iy0t7dChQ46OjnxsvJ41aADYsgXNmqF3b6HrqJXo6Ojc3NzJ3BVeCABg3rx5vr6+\n3bt3F7oQEXn//ffj4uJMTEyELkRE+vbte/jwYaGr0JJ6mEFz4QYhhOi6ehngEkKIFFCDJoQQkaIG\nTQghIkUNmhBCRIoatDD09fX19fWFrkJc9PT09OrnrHb+6Ovr0xVVKpDUVSvr4TQ7nVBaWqpUKukK\nT+UVFBSYmZlRPyovLy+vYcOGQlchLpIaE2rQhBAiUnRESQghIkUNmhBCRIoaNCGEiBQ1aEIIESlq\n0IQQIlLUoAkhRKSoQRNCiEhRgxbA2bNnO3XqZGtrO2bMmKKiIqHLEQWVSuXp6Xnz5k2hCxGLHTt2\nuLq6NmrUqG/fvjdu3BC6HFFYu3Zts2bNGjVq5OPj8/TpU6HL0QZq0NpWWlo6ZMiQBQsWPHjwIDc3\n95tvvhG6IuEdPXo0NDT07NmzQhciFunp6ePGjdu4cWNWVpaXl9fw4cPphLKUlJRPPvnk4MGDd+/e\nValUCxYsELoibaAGrW1HjhyxsbEZOnSomZnZ7Nmzo6Ojha5IeKdOndLX16frhpQ5depUly5devbs\nqa+vP2vWrBs3buTm5gpdlMBOnz7ds2fPVq1aWVtbjx49+tq1a0JXpA0SWnZEJO7du9e2bVvudtu2\nbe/du6dUKiW+SNCcOXMAxMfHC12IWAwYMKD33xd1O378ePPmzRs1aiRsSYIbPXr06NGj5XJ5SkrK\n7t2733nnHaEr0gZq0NqWk5NTttRLw4YN5XJ5fn6+hYWFsFURUTE3Nzc3N1epVAkJCZMmTVq9ejWt\nIcVJTEwcNWqUpaXl+fPnha5FG6hBa5uVlVV+fj53Oy8vT19f39zcXNiSiAhlZ2eHhoYmJyfv3Lmz\nV69eQpcjFsOGDRs0aFBUVNT7779/6dIlocvhnaSPrAXRokWLlJQU7nZKSkrz5s0lnm8QVklJiZeX\nl52d3ZUrV6g7c9auXbtp0yYAxsbGI0eOvHr1amlpqdBF8Y5aw/+3d/8hTX19HMCP7pdWU5lrS6dZ\nZmW4lCm5lNLSpDDNiWK/A0shUCSIEEEiJKzMJE3wH6mUCrNA1+qPFLWSmM7UrJGZWv6YhTozM3S6\nu+37x30Ywnx8fIjW5ev79de553x27jkX9t64m87e9uzZMzo6+uLFC4qiSkpKjh8//rdXBIyjVCpN\nJlNRUZHZbDYYDAaDAd/iEIlE169fHx8fN5vNZWVlcrmcw+H87UX9cbjFYW8cDkepVKanp09MTERF\nReXk5PztFQHjtLe3d3R0ODs7W3smJydX+OeEiYmJ7e3tQUFBFEWFhITcu3fvb6/IHvAP+wEAGAq3\nOAAAGAoBDQDAUAhoAACGQkADADAUAhoAgKEQ0AAADIWABgBgKAQ0AABDIaABABgKAQ0AwFAIaAAA\nhkJAAwAwFAIaAIChENAAAAyFgAYAYCgENAAAQyGgAQAYCgENAMBQCGgAAIZCQIM9/Pjxw8HBgcVi\nsdlsLpcrk8mam5sJIdHR0Ww2m81mW0fZbLZOp6uoqAgPD1+zZs3mzZtv3ry56C9nstnsgYEB62F5\nefm+ffvodk9Pz8GDB9euXSsSiRQKRX9/P93v5uZGn8XZ2Xnnzp1NTU2203p5edE1LBaLz+fHxsZ+\n/fp1ia2x2fjlZfhTENBgPxMTExRF9fb2+vv7Hz582GKxNDQ0UBRFUZSPj8/Lly/pdlVV1ZUrV27c\nuKHX6+/fv19cXHz79u3ln8VsNsfFxe3evXtkZGRoaEgmkyUmJlpHu7q6KIoaGxvLyMhQKBQdHR22\nM7x+/ZqiKJPJ9OXLF4vFkpub+5sbXzriAf4bBDTYm4+PT35+vl6vn5+ftx2dnJy8fPnyo0ePwsLC\nnJycQkNDCwsLa2pqlj//yMhIX19fVlYWl8t1cnLKzc319vaenp5eWMPn80+ePJmRkVFQULDEVEKh\nMDExcWhoiD5sbGwMDAwUi8UpKSk6nY4QEh8fbzKZpFJpQ0PDrl276LKWlha6rdVqIyMjjx49GhUV\nRbcLCgoSEhL8/PyeP39OCKEo6uzZs0KhUCgUXrx4cfl7hBUCAQ32Njo6WllZeeTIER6PZzva2trq\n5eW1fft2a09SUtLTp0+XP79EIpFIJKmpqW/evDGbzSwW69mzZ3w+37bywIEDi76Dtvr8+XNtbW1C\nQgIhZHx8PCUlpbS0VKfTbdy48dSpU4QQlUrFYrG0Wu2ieyGEtLS0BAYGtrW10e2goCClUpmbm3vp\n0iVCSE1NjVqt7unpaW1tLSws7OnpWf42YSVAQIP9uLu7s9lsT0/PvLw8hUKxaM3g4KBEIvmdszg6\nOjY3N/N4vJiYmHXr1qWmpg4ODi5aKRKJFr35EBER4eTkxOPxNm3aRFFUZmYmIeTJkycxMTEREREc\nDicvL0+j0ZjN5v+5GD6fn52dTb88CASC/fv3E0Lkcjn9jp6iqF+/fg0MDPj6+v78+XPLli2/s3H4\n90FAg/3Q96ApitJoNMeOHevs7LStEYvFo6OjC3tmZ2erqqrm5+fLy8v9/Pz8/Pyqq6uXOMv8/LyH\nh0dlZaVer1epVGKxOCAg4NOnT7aVY2NjHh4etv2vXr0yGAxzc3Pd3d0jIyMVFRWEkOHh4fr6eqlU\nKpVKQ0JCNmzY8P3790UXsPAjTZFI5Oj4n2eZQCCgGw4ODnQjOTk5PT09Li5u/fr1RUVFRqNxiX3B\nCoSABntzcHAICQmRy+Vqtdp2dMeOHb29vQvztKmp6fz58xwOJy0tra+vr6+vLyUlhRAiEAgmJias\nZXq9XigUEkJqamri4uIIISwWSy6XX716VSaTLXqu+vr64ODgJZbq7++vUCjevXtHCBGLxfHx8Vqt\nVqvVdnV1PX782N3dfWGxyWSiG9++fbN2WtOZLMhlq/Hx8dOnT+t0uurq6rt376pUqiUWAysQAhrs\nzWKxfPjwoa2tTSaT2Y5KJJKsrKykpCSNRmM0GrVa7YULFzIzM23TLSEhIScnZ3BwkKIotVpdUlKS\nnJxMCImMjOzs7CwtLZ2enjYajXV1dd3d3WFhYQsfOzMz8/Dhw1u3bmVnZy+9WoFAMDw8TAiJjY1V\nqVSdnZ1Go/HatWtpaWnWJRkMBhcXl7dv3w4NDc3OzpaVlS3zUlRWVh46dGh2dnbbtm18Pn9qamqZ\nD4SVwgLw501OThJCuFwuj8fjcrkSiaS4uHhhgY+PT3NzM902m80lJSUymWz16tW+vr75+flGo9F2\nzunp6XPnznl7e69atUoqld65c8c6pNFooqOjXV1d3dzcwsPD6+rq6H5XV1cOh8Pj8ZydnUNDQxsb\nG22nlUgkarXaeqhUKkUi0dTUlMViqa2t3bp1q5ub2969e/v7++kChULh6ek5MzOTnp7u4uISHBz8\n4MGDEydOWCyW9+/fBwQE0GUL2x8/fszMzKQvS2xsrIuLi7u7+5kzZ+bm5v7/Swv/Zg6Wxf4EAAAA\n/jrc4gAAYCgENAAAQyGgAQAYCgENAMBQCGgAAIZCQAMAMBQCGgCAoRDQAAAMhYAGAGAoBDQAAEMh\noAEAGAoBDQDAUAhoAACGQkADADAUAhoAgKEQ0AAADIWABgBgKAQ0AABD/QOrKRAb/6SmbAAAAABJ\nRU5ErkJggg==\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%R\n",
    "plot(y = Rt, x = Rb,\n",
    "    pch = 20, cex = 0.5,\n",
    "    xlab = \"BTC-USD Returns\",\n",
    "    ylab = \"Return Series 1\",\n",
    "    main = \"Return Series 1 vs. BTC-USD\")\n",
    "grid()\n",
    "abline(h = 0)\n",
    "abline(v = 0)\n",
    "\n",
    "# simple regression model which will have both intercept and the beta coefficient\n",
    "model <- lm(Rt ~ Rb)\n",
    "\n",
    "abline(model,col = 2)\n",
    "legend(x = \"topleft\", col = c(0,2), lwd = 2,\n",
    "      legend = c(\"Alpha Beta R^2\",\n",
    "                paste0(round(model$coefficients[1],4),\" \",\n",
    "                      round(model$coefficients[2],2), \" \",\n",
    "                      round(summary(model)$r.squared,2))))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The way the Return Series was generated was based on a small random noise from the original `BTC-USD` values thus the $\\alpha$ value is near 0 and the beta value is 1 with high correlation (i.e. $R^2 = 0.78$)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to illustrate how Jensen's $\\alpha$ works, negative returns will be replaced with a positive constant to demonstrate that with positive returns on the negative days the $\\alpha$ value will be much higher."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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44cOHDMN89dVX7P4///yzffv2Bw4cYF/m5ubOmDFjz549hYWF7u7u48aNU+p0GyUOEpQ4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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%R\n",
    "RtTemp <- c(0, Rt[-1]) # here we are getting rid of the first value by using the '-' notation\n",
    "\n",
    "# add 0.015 to all negative values and run regression again\n",
    "RtTemp[RtTemp < 0] <- RtTemp[RtTemp < 0] + 0.015\n",
    "model <- lm(RtTemp ~ Rb)\n",
    "\n",
    "plot(y = RtTemp, x = Rb,\n",
    "    pch = 20, cex = 0.5,\n",
    "    xlab = \"BTC-USD Returns\",\n",
    "    ylab = \"Return Series 1 with no negative returns\",\n",
    "    main = \"Return Series 1A vs. BTC-USD\")\n",
    "grid()\n",
    "abline(h = 0)\n",
    "abline(v = 0)\n",
    "\n",
    "\n",
    "abline(model,col = 2)\n",
    "legend(x = \"topleft\", col = c(0,2), lwd = 2,\n",
    "      legend = c(\"Alpha Beta R^2\",\n",
    "                paste0(round(model$coefficients[1],4),\" \",\n",
    "                      round(model$coefficients[2],2), \" \",\n",
    "                      round(summary(model)$r.squared,2))))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can clearly see that the value of $\\alpha$ has changed from negative to positive. This is indicative of the increase in $\\alpha$ when a strategy is able to reduce the impact of losing days by an average of 1.5 percent. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another metric that we can take a look at is Pure Profit Score (PPS) which describes risk and return by multiplying the total account return by the $R^2$ of a regression of a linearized equity curve against time. \n",
    "$$ \\text{PPS} = \\frac{E_{T_0} - V_0}{V_0}R^2 $$\n",
    "Where the numerator of the fraction on the RHS indicates the total account return and the second portion after the fraction is the correlation of the equity curve $R^2$ linearized by dividing by the tradable account $V_t$ for time $t = 0,1,\\dots,T$.\n",
    "$$\\frac{E_{t_0}}{V_t} = \\alpha + \\beta t + \\epsilon_t$$\n",
    "Since the vector $V_t$ in our case is constant, the linearization is trivial."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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WW2DSp08ftF2sM88///zzzz/fpsHwVqykpKQ4H3Hbi0zAEoe42Gy20GzjKVOJ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\nBZpCoVC6KVSgKRQKpZvy/0m5/RSZITg0AAAAAElFTkSuQmCC\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%R\n",
    "# create linearized equity curve and run regression\n",
    "y <- Et/Vt\n",
    "y2 <- Et2/Vt\n",
    "yb <- Eb/Vt\n",
    "modelta <- lm(y ~ t)\n",
    "modelt2a <- lm(y2 ~ t)\n",
    "modelba <- lm(yb ~ t)\n",
    "# Compute the PPS by using the r.squared in the summary(model) attributes\n",
    "PPS <- ((Et[length(Et)] - Vt[1]) / Vt[1]) * summary(model)$r.squared # here since we are using the final market close return the last Et will be E_{T_0}( i.e unadjusted)\n",
    "PPS1 <- ((Et2[length(Et2)] - Vt[1]) / Vt[1]) * summary(model1)$r.squared # here since we are using the final market close return the last Et will be E_{T_0}( i.e unadjusted)\n",
    "PPSb <- ((Eb[length(Eb)] - Vt[1]) / Vt[1]) * summary(modelb)$r.squared # here since we are using the final market close return the last Et will be E_{T_0}( i.e unadjusted)\n",
    "\n",
    "# This is for the regression on the return on benchmark not on time to calculate the PPS\n",
    "modeltb <- lm(Rt ~ Rb)\n",
    "modelt2b <- lm(Rt2 ~ Rb)\n",
    "modelbb <- lm(Rb ~ Rb)\n",
    "\n",
    "plot(y = Et, x = t, type = \"l\", col = 1,\n",
    "    xlab = \"Time\",\n",
    "    ylab = \"Equity ($)\",\n",
    "    main = \"Randomly Generated Equity Curves\",\n",
    "    ylim = c(0, 2.5e6))\n",
    "grid()\n",
    "abline(h = 1e4)\n",
    "lines(y = Et2, x = t, col = 2)\n",
    "lines(y = Eb, x = t, col = 8)\n",
    "legend(x = \"topleft\", col = c(0,1,2,8), lwd = 2, legend = c(\"Alp Bet R^2 PPS\",\n",
    "                                                           paste0(round(modeltb$coefficients[1],2),\" \",\n",
    "                                                                  round(modeltb$coefficients[2],2), \" \",\n",
    "                                                                  round(summary(modeltb)$r.squared,2), \" \",\n",
    "                                                                 round(PPS, 2)),\n",
    "                                                           paste0(round(modelt2b$coefficients[1],2),\" \",\n",
    "                                                                  round(modelt2b$coefficients[2],2), \" \",\n",
    "                                                                  round(summary(modelt2b)$r.squared,2), \" \",\n",
    "                                                                 round(PPS1, 2)),\n",
    "                                                           paste0(round(modelbb$coefficients[1],2),\" \",\n",
    "                                                                  1, \" \",\n",
    "                                                                  round(summary(modelbb)$r.squared,2), \" \",\n",
    "                                                                 round(PPSb, 2))\n",
    "                                                          ))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Final Comments"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Optimizing Performance Metrics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The fundamental goal of trading is the **Maximize Risk-Adjusted Return**. The goal of strategy development would be to aid in maximizing the goal of trading. In order to do that we will:\n",
    "- Use Cross Validation (CV) methods\n",
    "- Utilize both simple and complex models that will best predict future prices and thereby allow the algorithm to buy and sell accordingly"
   ]
  }
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